This paper studies the optimal taxation between luxury and necessity goods. We set up a three-production-sector neoclassical growth model with inelastic labor supply, and analyze the tax incidence. We find that the two consumption taxes are neutral to economic growth and that the welfare maximization optimal tax mix involves levying the same rate on those two goods. In reality, the tax rate levied on the luxury good is usually higher, so that the government should reduce the tax rate on the luxury good and raise that on the necessity good to the same level in order to enhance the household's lifetime welfare.